Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 33462.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33462.v1 | 33462bd2 | \([1, -1, 0, -13628952, 19507556160]\) | \(-2785800837625/23068672\) | \(-2318374789210976550912\) | \([]\) | \(2044224\) | \(2.9262\) | |
33462.v2 | 33462bd1 | \([1, -1, 0, 508743, 141741549]\) | \(144896375/170368\) | \(-17121786468171884928\) | \([]\) | \(681408\) | \(2.3769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33462.v have rank \(1\).
Complex multiplication
The elliptic curves in class 33462.v do not have complex multiplication.Modular form 33462.2.a.v
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.